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We consider n die whose faces are numbered from 1 to 5. If those dice are fair, the probability that a certain sum, denoted by p, of the n dice sides to occur is defined by P(p,n,s)

Now, if we assume that all the sides of the dice have the same probability to occur which is 25/124 except the face number 3 which have a probability 24/124. We verify that the sum of probabilities is (25*4+24)/124 is equal to 1. What becomes the formula above in this case?

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  • $\begingroup$ What are the meanings of $k$ and $k_{max}$ ? $\endgroup$ – callculus Apr 16 '17 at 15:34
  • $\begingroup$ kmax = floor((p-n)/s) or simply the result of the euclidean division of (p-n) by s $\endgroup$ – Rami Zouari Apr 16 '17 at 16:10
  • $\begingroup$ And what is the meaning of k ? $\endgroup$ – callculus Apr 16 '17 at 16:12
  • $\begingroup$ it's simply a sum index which takes the values between 0 and kmax. for example for n = 2, s = 5 and 2 <= p < 7, k can be just 0, and for 7<= p <= 10, k can be 0 or 1 $\endgroup$ – Rami Zouari Apr 16 '17 at 16:17
  • $\begingroup$ mathworld.wolfram.com/Dice.html $\endgroup$ – Rami Zouari Apr 16 '17 at 17:16
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Anyway, i found the solution alone P(p,n,s) where s²/(s^3-1) = 25/124 and (s²-1)/(s^3-1) = 24/124 here the plot for n = 2 plot

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